<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>meshGrid</title>
<style type="text/css">
	body {background-color: white; color: black; font-family:sans-serif; font-size:medium;}
	a:link {color: #3300ff;}
	a:visited {color: #663399;}
	a:hover {color:#0099ff;}
	a:active {color: #0066cc;}
	a.button {text-decoration:none;}
	
	table.nav  {background-color: #dbddff;}
	table.body {margin-top:2ex; margin-bottom:2ex;}
	table.programlistingindent {margin-left:32px;}
	
	img { margin-bottom:0px; margin-top:0px;}
	tt {margin-left:0.5em; margin-right:0.5em; font-weight:lighter;}
	
	p {margin-top:0ex;}
	p.synopsis {margin-left:32px;}
	p.programlistingindent {margin-left:32px;}
	p.citetitle {margin-left:2em;}
	
	ul ul {list-style-type:square;}
	ul li p {margin-top:0ex; margin-bottom:.5ex; padding:0}
	ol li p {margin-top:0ex; margin-bottom:.5ex; padding:0}
	
	h1.reftitle {color:#a90000;}
	h1.reftitle {font-size:3.7ex; margin-top:0; margin-bottom:0; font-weight:bold}
	h1.title {color:black; font-size:4ex; margin-top:1ex; font-weight:bold}
	h2.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:3ex}
	h3.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2.5ex}
	h4.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2ex}
	h2 {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2.5ex}
	h3 {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2ex} 
	
	pre.programlisting {margin-left:32px;}
	pre.synopsis {margin-left:32px;}
	
	
	.categorytitle {margin-top:8px; padding-top:0px;}
	.categorylist {background-color: #e1e6f2;}
 	</style>
</head>
<body>
<a name="top_of_page"></a><p style="font-size:1px;"></p>
<h1 class="reftitle">meshGrid</h1>
<h2>Purpose</h2>
<p>Generate X-Y grid for 2D bounded polyhedra.</p>
<h2>Syntax</h2>
<pre class="synopsis">[X,Y] = P.meshGrid</pre>
<pre class="synopsis">[X,Y] = P.meshGrid(N)</pre>
<pre class="synopsis">[X,Y] = meshGrid(P,N)</pre>
<h2>Description</h2>
<p></p>
        Generates X-Y grid points for plotting of two-dimensional polyhedra. Supported are only bounded and
        lower-dimensional polyhedra.   
        
        The output from this function is consistent with Matlab "meshgrid" function used for plotting functions
        over 2D polyhedra. The argument to this function is the number of points used to grid the polyhedron, 
        default value is 20.      
<h2>Input Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody>
<tr valign="top">
<td><tt>P</tt></td>
<td>
<p></p>Polyhedron given by V- or H-representation in dimension 2.<p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>N</tt></td>
<td>
<p></p>The number of points for gridding. The value must be positive and integer-valued.<p>
	    		Class: <tt>double</tt></p>
<p>
	    		Default: 20</p>
</td>
</tr>
</tbody>
</table>
<h2>Output Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody>
<tr valign="top">
<td><tt>X</tt></td>
<td>
<p></p>Matrix with x-coordinates of the grid values.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>Y</tt></td>
<td>
<p></p>Matrix with y-coordinates of the grid values.<p>
	    		Class: <tt>double</tt></p>
</td>
</tr>
</tbody>
</table>
<h2>Example(s)</h2>
<h3>Example 
				1</h3>Define random polyhedron <tt>P</tt> in 2D.<pre class="programlisting"> P = ExamplePoly.randVrep; </pre>
<pre class="programlisting"></pre>Grid the polyhedron <pre class="programlisting">[X,Y] = P.meshGrid; </pre>
<pre class="programlisting"></pre> Define Z coordinate as <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/meshgrid1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/meshgrid1.png">. <pre class="programlisting"> Z=10./(1+exp((X-Y).^2)); </pre>
<pre class="programlisting"></pre>Plot the Polyhedron and the Z values.<pre class="programlisting"> plot(P,'color','limegreen','alpha',0.4); hold on; surf(X,Y,Z); view(3); </pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/meshgrid_img_1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/meshgrid_img_1.png" width="60%"></p>
<h2>See Also</h2>
<a href="../@ConvexSet/grid.html">grid</a>, <a href="../@ConvexSet/plot.html">plot</a>, <a href="../@ConvexSet/fplot.html">fplot</a><p></p>
<table class="nav" summary="Navigation aid" border="0" width="100%" cellpadding="0" cellspacing="0"><tr valign="top">
<td align="left" width="20">
<a href="be.html" class="button">&#9664;</a>  </td>
<td align="left">be</td>
<td>  </td>
<td align="right">ge</td>
<td align="right" width="20"><a href="ge.html" class="button">&#9654;</a></td>
</tr></table>
<br><p>©  <b>2010-2013</b>     Colin Neil Jones: EPF Lausanne,    <a href="mailto:colin.jones@epfl.ch">colin.jones@epfl.ch</a></p>
<p>©  <b>2010-2013</b>     Martin Herceg: ETH Zurich,    <a href="mailto:herceg@control.ee.ethz.ch">herceg@control.ee.ethz.ch</a></p>
</body>
</html>
